Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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find the area. 12 ft 18 ft a = ? ft²
108
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find the area. 12 in 18 in a = ? in²
108
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find the perimeter. 34 m 20 m 34 m p = ? m
88
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find the area. 9 in 7 in a = ? in²
63
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find the area. 30 m 25 m a = ? m²
750
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magnifying glass 5.2 cm 16 cm car tire 23 in 71.6 in part b complete th…
The given diameters are multiplied by the constant of proportionality (\(\pi\approx3.14\)) to find the missing circumferences. The given circumferences are divided by the constant…
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find the perimeter. 63 cm 18 cm p = ? cm
162
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find the distance, d, of \\( \\overline { a b } \\). \\( a = ( - 7,9 ) …
\(6.3\)
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find the midpoint, m, of \\( \\overline { a b } \\). \\( a = ( 3,7 ) b …
$(5,9)$
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part a complete the table. use one of the approximate values for π disc…
| Object | Diameter | Circumference | |--|--|--| | Hula Hoop | \(35\) in | \(110\) in | | Circular Pond | \(177\) ft | \(556\) ft | | Magnifying Glass | \(5.2\) cm | \(16\) cm | |…
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diego measured the diameter and circumference of several circular objec…
The measurement should be about three times the diameter.
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what does the following notation describe? overline{ab} || overline{dc}…
two parallel segments
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two lines are parallel if they: never intersect. intersect in 90 degree…
A. never intersect.
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if ∠efg and ∠lmn are complementary, and m∠efg is equal to 32°, then wha…
$58$
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if ∠efg and ∠lmn are vertical angles, and m∠efg is equal to 38°, then w…
\(38\)
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if ( mangle abc = 122^{circ} ) and ( mangle abd = 71^{circ} ), then ( m…
$51$
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if ( mangle abc = 125^{circ} ) and ( mangle abd = 94^{circ} ), then ( m…
$31$
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what is the measure of this angle? m∠abc = ?°
35
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if ab = 20 and bc = 31, find ac. a b c 20 31 ac = ?
51
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find the midpoint, m, of (overline{ef}). e m f 6 18 (m=) ?
$12$
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what is the correct notation for this figure? y z yz yz yz
\(\overline{YZ}\)
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postulate #2: if two distinct lines intersect, then their intersection …
B. 2
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unit exam - tools of geometry there is one and only one line that passe…
B. The points are noncollinear
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which figure fits this geometric notation? yx
First figure (with points \(Y\) and \(X\) on a line with arrows in both directions)
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this figure is the net of which geometric solid? a cube a rectangular p…
C. A square - based pyramid
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this figure is the net of which geometric solid? a triangle - based pyr…
C. A cube
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1. which of the following represents the solution for $5x - 3 leq 32$ 2…
1. For \(5x - 3\leq32\), the solution is represented by option B (assuming option B has a closed circle at \(7\) and the line to the left). 2. For \(7x - 2\lt54\), the solution is…
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1. solve the following inequality for c. graph it on the number line. 2…
The solution is \(c > - 1\). To graph it on the number line: draw an open circle at \(-1\) (because the inequality is strict, \(c eq - 1\)) and shade the line to the right of \(-…
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \(x\leq8\). On the number - line, plot a closed circle at 8 (because the inequality includes equality, \(\leq\)) and draw a line to the left of 8.
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \(x\leq7\) For the number - line: Place a closed circle at \(x = 7\) (because the inequality is \(\leq\)) and shade to the left of \(7\) (since \(x\) is less …
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \(x\lt - 2\) For the number line: Place an open circle at \(-2\) (because the inequality is strict, i.e., \(x eq - 2\)) and shade the line to the left of \(-…
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \(x\leq2\) To graph on the number - line: Place a closed circle at \(x = 2\) (because the inequality is \(\leq\)) and draw a line to the left of \(2\) towards…
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for questions 3 - 6, state the angle relationship(s) needed to find the…
\(107^{\circ}\)
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2) lines rs and tv intersect to form angles 1, 2, 3 and 4. the measure …
C. \(m\angle1 = 130^{\circ};m\angle3 = 50^{\circ};m\angle4 = 50^{\circ}\)
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find the lateral surface area of the cylinder. lsa = ? cm² round to the…
\(87.92\)
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find the lateral surface area of the cylinder. lsa=square cm^{2} round …
\(753.6\)
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find the lateral surface area of the prism. lsa =? cm²
\(128\)
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using eulers formula, how many edges does a polyhedron with 8 faces and…
\(14\)
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find the number of edges on this solid.
18
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what is the probability that a random point on \\overline{ab} will be o…
\(0.33\)
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solve for x. round to the nearest tenth, if necessary.
\(0.8\)
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15. why should you take notes when doing research? because its part of …
to record and remember information accurately
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jessica is looking at a map of her property on the coordinate plane. th…
\(9.9\)
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5. elena needs to prove angles bed and bca are congruent. ∠bde ≅ ∠bac p…
a. Converse of the corresponding angles postulate. b. Corresponding angles postulate.
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4. when triangle abc is reflected across line ab, the image is triangle…
b. Corresponding parts of congruent figures are congruent.
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3. triangle hef is the image of triangle fgh after a 180° rotation arou…
B. Triangle \(EFH\) is congruent to triangle \(GFH\); D. Angle \(GHK\) is congruent to angle \(KHE\); E. Segment \(EH\) is congruent to segment \(FG\); F. Segment \(GH\) is congru…
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what is the scale factor from figure a to figure b? draw show your work…
\(3\)
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what is the scale factor from figure a to figure b? draw figure a figur…
\(6\)
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each column of the matrix ( a=\begin{bmatrix}1&6&6&1\\1&1&5&5end{bmatri…
\((4,4)\), \((24,4)\), \((24,20)\), \((4,20)\) (corresponds to the first option)
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find the perimeter (circumference) and the area of each figure
- **Left Figure (Circle)**: - Circumference: \(2\pi\sqrt{13}\approx22.67\) - Area: \(13\pi\approx40.82\) - **Right Figure (Triangle)**: - Perimeter: \(\sqrt{61}+\sqrt{29}+8\approx…
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refer to the figure at the right if <2 = 7x +15 and <3 = 5x + 35, find …
\(x = 10\), \(\angle2=85^{\circ}\), \(\angle3=85^{\circ}\)
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which of the following conditions must be met to use the sss triangle c…
1. c. All three pairs of corresponding sides must be equal. 2. a. Their perimeters will be equal. 3. c. It ensures all sides are equal, allowing parts to fit together perfectly. 4…
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which of the following properties is always true for triangles proven c…
1. A. Their corresponding sides and angles are equal 2. C. The triangles are congruent by SSS 3. D. 6 cm, 7 cm, 10 cm 4. D. Side - Side - Side 5. B. Their corresponding angles are…
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read the sentences below, filling in the blanks with items from this li…
1. congruent 2. SSS 3. measure 4. compare 5. angles 6. accuracy 7. measurement
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use the number line to represent the solution to 2.4x - 6 > -13.2. sele…
Select the ray with an open circle at \(-3\) and pointing upwards (assuming the number line is vertical as in the given image).
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δabc ~ δxyz a 14.4 b y 5 z x 12 13 c x y 14.4/12 = 1.2
\(x = 6\), \(y=15.6\)
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are the vectors orthogonal? \\( \\langle 3, - 9 \ angle, \\langle - 6, …
Yes
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if $\\mathbf{u}=\\langle -5,7\ angle$, $\\mathbf{v}=\\langle -3,6\ angl…
\(126\), so the answer is B.
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if ( mathbf{u}=langle-3,5 angle ) and ( mathbf{v}=langle 4,4 angle ), e…
D. \(16\)
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find the magnitude and direction angle (to the nearest tenth) for each …
A. \(12;150^{\circ}\)
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find the area of a triangular garden if the sides are approximately 4 f…
B. \(24\mathrm{ft}^2\)
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find the area of triangle abc with the given parts. round to the neares…
B. \(1,182\ ft^{2}\)
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find the measure of angle a. a. 60° b. 135° c. 120° d. 140°
C. \(120^{\circ}\)
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find the missing parts of the triangle. a. b = 90°, c = 60°, b = 9√3 b.…
D. \(B = 60^{\circ},C = 90^{\circ},b = 9\sqrt{3}\)
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solve the triangle. round to one decimal places. a. c = 103°, a = 17.5 …
C. \( C = 103^{\circ},a = 9.9\) m, \(b = 17.5\) m
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determine the number of triangles abc possible with the given parts. a …
B. 1
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find the magnitude and positive direction angle of the vector $\\langle…
\(210\)
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find the magnitude and positive direction angle of the vector $\\left\\…
\(8\)
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write the vector ( u = langle 8,-9 angle ) in ( mathbf{i}, mathbf{j} ) …
\(8\vec{i}-9\vec{j}\)
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apply 16. a rectangle has a length that is half its width. define a var…
Let \( w \) be the width of the rectangle. The perimeter \( P = 3w \). ### 17.
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apply 16. a rectangle has a length that is half its width. define a var…
Let \( w \) be the width of the rectangle. The expression for the perimeter is \( 3w \).
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refer to the vectors m through t at the right. name all pairs of vector…
B. m and q; n and s
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refer to the vectors m through t at the right. name all groups of vecto…
C. \(m\) and \(p\); \(n\) and \(r\)
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two ships leave a harbor together traveling on courses that have an ang…
B. 931 mi
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two points a and b are on opposite sides of a building. a surveyor choo…
D. 85 yd
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find the length of side a. a. 7 b. \\( \\sqrt { 47 } \\) c. \\( \\sqrt …
A. 7
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find the length of side a. a. 1 b. \\sqrt{13} c. \\sqrt{61} d. \\sqrt{7…
B. \(\sqrt{13}\)
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examining the relationship between angle measures and side lengths drag…
1. If the angle measure is the largest of the triangle, the side opposite is the longest length. 2. If a side is the shortest of the triangle, the angle opposite that side is the …
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find the missing parts of the triangle. a. ( a = 45^{circ}, c = 75^{cir…
A. \(A = 45^{\circ},C = 75^{\circ},c = 3\sqrt{3}+3\)
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find the missing parts of the triangle. oa. b = 60°, c = 90°, b = 4√3 o…
C. No such triangle exists.
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did you hear the story about the piece of butter? complete each exercis…
A. \(90\) (NEVER), B. \(102\) (WANT), C. \(46\) (no match in the key, but if we assume a typo), D. \(35\) (no match), E. \(45\) (SPREAD), F. \(114\) (IS A BIT), G. \(29\) (IT), H.…
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determine the number of triangles abc possible with the given parts. a …
D. 0
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identifying angles of a triangle given (\triangle ghj), complete the fo…
The included angle of sides \(JG\) and \(GH\) is \(\angle G\). Angle \(H\) is the opposite angle to side \(JG\). The side opposite to \(\angle J\) is side \(GH\).
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a farmer has 28 baskets of apples already and can pick 6 baskets of app…
The inequality is \(28 + 6d>50\) and the solution is \(d>\frac{11}{3}\). On a number - line, we draw an open circle at \(\frac{11}{3}\) (or approximately \(3.67\)) and shade to th…
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select the correct answer. the surface area of a sphere is approximatel…
B. 6.8 feet
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what value of x proves that the lines m and l are parallel in each of t…
\(x\approx1.85\)
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triangle qrs has the angle measures shown. ( mangle q=(1x)^{circ} ) ( m…
\(108\)
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a triangle has side lengths measuring ( 2x + 2 ) ft, ( x + 3 ) ft, and …
\(x - 1\lt n\lt3x + 5\)
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3 select the correct answer. franco has enough paint to cover an area o…
B. 4 feet
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triangle abc is an obtuse triangle with the obtuse angle at vertex b. a…
C. less than \(90^{\circ}\)
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2 select the correct answer. sophia has unsharpened pencils that are 20…
B. \(60\mathrm{cm}^2\)
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which are the possible side lengths of a triangle? 4 cm, 8 cm, 10 cm 8 …
\(4\ cm, 8\ cm, 10\ cm\)
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iliana claims that she can construct a triangle from a 12 - inch rod, a…
Iliana will be able to construct a triangle because the sum of any two sides is greater than the third side.
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a triangle has side lengths measuring ( 3x ) cm, ( 7x ) cm, and ( h ) c…
\(4x < h < 10x\)
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in triangle xyz, ( mangle z>mangle x + mangle y ). which must be true a…
\(m\angle X + m\angle Y<90^{\circ}\) (the second option)
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if triangle def has a 90° angle at vertex e, which statements are true?…
- Triangle \(DEF\) is a right - triangle. - The angle at vertex \(D\) is acute.
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triangle qrs is a right triangle with the right angle at vertex r. the …
equal to \(90^{\circ}\)
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the diagram shows the aerial view of a park. what is the length of the …
D. 309 yards
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did you hear the story about the piece of butter? complete each exercis…
A. \(53\) (not in the right - hand column), B. \(107\) (MIND), C. \(41\) (I), D. \(88\) (not in the right - hand column), E. \(122\) (WANT), F. \(124\) (TO), G. \(45\) (SPREAD), H…
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applying the triangle inequality theorem in triangle abc, ab measures 2…
The first inequality is \(10\lt s\lt60\) and the second inequality is \(70\lt p\lt120\).